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This paper presents a new discriminative language model based on the whole-sentence maximum entropy (ME) framework. In the proposed discriminative ME (DME) model, we exploit an integrated linguistic and acoustic model, which properly incorporates the features from n-gram model and acoustic log likelihoods of target and competing models. Through the constrained optimization of integrated model, we estimate DME language model for speech recognition. Attractively, we illustrate the relation between DME estimation and the maximum mutual information (MMI) estimation for language modeling. It is interesting to find that using the sentence-level log likelihood ratios of competing and target sentences as the acoustic features for ME language modeling is equivalent to performing MMI discriminative language modeling. In the experiments on speech recognition, we show that DME model achieved lower word error rate compared to conventional ME model.